Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers
This work addresses efficiency in distributed computing systems, particularly for data-intensive tasks like linear algebra, but it is incremental as it builds on prior coded computing approaches.
The paper tackles the problem of distributed matrix-vector multiplication with straggling servers by proposing two coded schemes: one using block-diagonal MDS codes to reduce encoding/decoding delay and another using LT codes to trade communication load for delay reduction. The results show that the LT code-based scheme outperforms existing methods in deadline scenarios, with numerical demonstrations of improved performance.
We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding and decoding delay) are identical to those of the scheme recently proposed by Li et al., based on a single, long MDS code. However, due to the use of shorter MDS codes, our scheme yields a significantly lower overall computational delay when the delay incurred by encoding and decoding is also considered. We further propose a second coded scheme based on Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes may reduce the delay over the partitioned scheme at the expense of an increased communication load. We also consider distributed computing under a deadline and show numerically that the proposed schemes outperform other schemes in the literature, with the LT code-based scheme yielding the best performance for the scenarios considered.